Problem Solving

If xy+z=x(y+z). which of the following mus be true?

A) x=0 , z=0

B) x=1 , y=1

C) y=1 , z=0

D) x=1 , y=0

E) x=1 , z=0

Given the info we should solve for any number here.
xy + z = x(y + z)
xy + z = xy + xz
z = xz
z/z = x
x = 1

We are down to choices B, D, E,
Check B. ==> X = 1, y = 1, z = 3
We will get equation 1*1 + 3 = 1(1 +3) ==> 4 = 4
Check when z = 0. ==> 1*1 + 0 = 1(1 + 0) ==> 1 + 0 = 1+ 0 ==> 1= 1
Works, but we have to check all other choices.
D. x = 1, y = 0, z = 3
1*0 + 3 = 1(0 + 3) ==> 1 +3 = 0 + 3 ==> 4 >3 DOES NOT work.
Check E.
x = 1, z = 0, y =3
1*3 + 0 = 1(3 + 0) ==> 3 + 0 = 3 + 0 ==> 3 = 3 Works.
But, what if y = 0? Then, 1*0 + 0 = 1(0 + 0) ==> 1 + 0 = 0 + 0 ==> 1> 0, DOES NOT work.
The answer must be B, because it works for all numbers, positive and negative.

Hmm.. was there more information in the stem? Did you mistype the choices? It doesn't seem like any of the choices are MUST be trues.

We could pick x=0, y=0, z=0

therefore, b, c, d and e aren't MUST be trues.

We could also pick x=1, y=1, z=1

therefore a isn't a MUST be true.

We've elminated a, b, c, d and e.. umm.. choose (f)?

Sorry there is a mistake here, I forgot to put "and" or "or" in the answer choices...for me it doesnt make any sense either. Here is how it is:

If xy+z=x(y+z). which of the following mus be true?

A) x=0 AND z=0

B) x=1 AND y=1

C) y=1 AND z=0

D) x=1 OR y=0

E) x=1 OR z=0

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